Boundary Value Problems

Author: David L. Powers
Publisher: Academic Press
ISBN: 0080884415
Format: PDF, ePub, Docs
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Boundary Value Problems, Sixth Edition, is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations. In this updated edition, author David Powers provides a thorough overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Additional techniques used include Laplace transform and numerical methods. The book contains nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises. Professors and students agree that Powers is a master at creating examples and exercises that skillfully illustrate the techniques used to solve science and engineering problems. Ancillary list: Online SSM- http://www.elsevierdirect.com/product.jsp?isbn=9780123747198 Online ISM- http://textbooks.elsevier.com/web/manuals.aspx?isbn=9780123747198 Companion site, Ebook- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747198 Student Solution Manual for Sixth Edition - https://www.elsevier.com/books/student-solutions-manual-boundary-value-problems/powers/978-0-12-375664-0 New animations and graphics of solutions, additional exercises and chapter review questions on the web Nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises Many exercises based on current engineering applications

An Introduction to Nonlinear Boundary Value Problems

Author: Lakshmikantham
Publisher: Academic Press
ISBN: 0080956181
Format: PDF, ePub, Mobi
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A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: methods that involve differential inequalities; shooting and angular function techniques; functional analytic approaches; topological methods.

Boundary Value Problems

Author: Chi Yeung Lo
Publisher: World Scientific
ISBN: 9789810243005
Format: PDF, ePub, Docs
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This book has been designed for a one-year graduate course on boundary value problems for students of mathematics, engineering, and the physical sciences. It deals mainly with the three fundamental equations of mathematical physics, namely the heat equation, the wave equation, and Laplace's equation. The goal of the book is to obtain a formal solution to a given problem either by the method of separation of variables or by the method of general solutions and to verify that the formal solution possesses all the required properties. To provide the mathematical justification for this approach, the theory of Sturm-Liouville problems, the Fourier series, and the Fourier transform are fully developed. The book assumes a knowledge of advanced calculus and elementary differential equations.

Boundary Value Problems

Author: F. D. Gakhov
Publisher: Elsevier
ISBN: 1483164985
Format: PDF, ePub, Mobi
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Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value are explained. The Riemann boundary value problem is emphasized in considering the theory of boundary value problems of analytic functions. The book then analyzes the application of the Riemann boundary value problem as applied to singular integral equations with Cauchy kernel. A second fundamental boundary value problem of analytic functions is the Hilbert problem with a Hilbert kernel; the application of the Hilbert problem is also evaluated. The use of Sokhotski's formulas for certain integral analysis is explained and equations with logarithmic kernels and kernels with a weak power singularity are solved. The chapters in the book all end with some historical briefs, to give a background of the problem(s) discussed. The book will be very valuable to mathematicians, students, and professors in advanced mathematics and geometrical functions.

Boundary Value Problems of Heat Conduction

Author: M. Necati Ozisik
Publisher: Courier Corporation
ISBN: 0486782867
Format: PDF, Docs
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Intended for first-year graduate courses in heat transfer, this volume includes topics relevant to chemical and nuclear engineering and aerospace engineering. The systematic and comprehensive treatment employs modern mathematical methods of solving problems in heat conduction and diffusion. Starting with precise coverage of heat flux as a vector, derivation of the conduction equations, integral-transform technique, and coordinate transformations, the text advances to problem characteristics peculiar to Cartesian, cylindrical, and spherical coordinates; application of Duhamel's method; solution of heat-conduction problems; and the integral method of solution of nonlinear conduction problems. Additional topics include useful transformations in the solution of nonlinear boundary value problems of heat conduction; numerical techniques such as the finite differences and the Monte Carlo method; and anisotropic solids in relation to resistivity and conductivity tensors. Illustrative examples and problems amplify the text, which is supplemented by helpful appendixes.

A Unified Approach to Boundary Value Problems

Author: Athanassios S. Fokas
Publisher: SIAM
ISBN: 0898716519
Format: PDF, Mobi
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A novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and the Dirichlet-to-Neumann map for a moving boundary; integral representations for linear boundary value problems; analytical and numerical methods for elliptic PDEs in a convex polygon; and integrable nonlinear PDEs. An epilogue provides a list of problems on which the author's new approach has been used, offers open problems, and gives a glimpse into how the method might be applied to problems in three dimensions.

Numerical Solution of Nonlinear Boundary Value Problems with Applications

Author: Milan Kubicek
Publisher: Courier Corporation
ISBN: 0486463001
Format: PDF
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A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.

Fourier Analysis and Boundary Value Problems

Author: Enrique A. Gonzalez-Velasco
Publisher: Elsevier
ISBN: 9780080531939
Format: PDF
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Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics. A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field. Topics are covered from a historical perspective with biographical information on key contributors to the field The text contains more than 500 exercises Includes practical applications of the equations to problems in both engineering and physics

Analytical Solution Methods for Boundary Value Problems

Author: A.S. Yakimov
Publisher: Academic Press
ISBN: 0128043636
Format: PDF, Mobi
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Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods. Discusses the theory and analytical methods for many differential equations appropriate for applied and computational mechanics researchers Addresses pertinent boundary problems in mathematical physics achieved without using the theory of series Includes results that can be used to address nonlinear equations in heat conductivity for the solution of conjugate heat transfer problems and the equations of telegraph and nonlinear transport equation Covers select method solutions for applied mathematicians interested in transport equations methods and thermal protection studies Features extensive revisions from the Russian original, with 115+ new pages of new textual content